Question

Assume a company has an annual dividend of $2.00 per share. It is expected to grow that dividend at a rate of 10% p.a. over the next two years and then at a rate of 7% p.a. thereafter. Assuming the market's required rate of return for this company's stock is 15% p.a.: its implied valuation using a dividend discount model is closest to:

A. $27.50
B. $28.20
C. $28.90
D. $29.70

Answer 1

PHASE 1

Growth rate (g) = 10% = 0.10

No of years (n) = 2 years

Cost of equity (Ke) = 15% = 0.15

Current dividend paid (Do) = $2

Dividend in 1 year’s time (D1) = Do(1+g)n

= $2(1 + 0.10)1

= $2.20

Dividend in 2 year’s time (D2) = Do(1+g)n

= $2(1 + 0.10)2

V1 = D1 + D2

(1 + K) (1 + K)2

V1 = $2.20 + $2.42

(1 + 0.15) (1 + 0.15)2

V1 = 2.20 + $2.42

1.15 1.15)2

V1 = $1.9130 + $1.8297

V1 = $3.7427

PHASE 2

g = 7% = 0.07

V2 = DN( 1 + g)

(Ke –g)(1+ K)n

V2 = $2.42(1 + 0.07)

(0.15 – 0.07)(1+ 0.15)2

V2 = $2.5894

(0.08)(1.15)2

V2 = $2.5894

(0.08)(1.3225)

V2 = $24.4745

Current market price = V1 + V2

= $3.74 + $24.47

= $28.21

The correct answer is B

Explanations:

In this case, there is need to calculate the current market price of equity in the first growth regime of 10%. The current market price is a function of dividend in 1 year’s time and dividend in year’s time divided by (1 + Ke)n.

In the second phase of growth, the growth rate is 7%. We need, to determine the current market price , which is a function of dividend in 2 year’s time, subject to the new growth rate divided by the product of K-g and (1+ K)n.

The current market price is the aggregate of market prices for the two growth regimes.